If water is being poured at the rate of $36 \text{ } m^3/sec$ into a cylindrical vessel with a base radius of $3 \text{ } m$,then the rate at which the water level is rising is:

The radius of a right circular cylinder increases at a constant rate. Its altitude is a linear function of the radius and increases three times as fast as the radius. When the radius is $1 \, cm$,the altitude is $6 \, cm$. When the radius is $6 \, cm$,the volume is increasing at the rate of $1 \, cm^3/sec$. When the radius is $36 \, cm$,the volume is increasing at a rate of $n \, cm^3/sec$. The value of $n$ is equal to:

Let a kind of bacteria grow following the function $f(t) = t^4$,where $t$ is given in seconds. If the rate of growth of the bacteria after $t_0$ seconds is $4000 \text{ units/second}$,then $t_0 =$

$A$ spherical iron ball of $10 \ cm$ radius is coated with a layer of ice of uniform thickness that melts at a rate of $50 \ cm^3/min$. When the thickness of ice is $5 \ cm$,then the rate (in $cm/min$) at which the thickness of ice decreases is:

$A$ ladder of length $10 \ m$ is resting against a vertical wall. The bottom of the ladder is pulled along the ground away from the wall at the rate of $2 \ m/min$. How fast is its height on the wall decreasing when the foot of the ladder is $6 \ m$ away from the wall?

$A$ particle is moving on a straight line. The distance $S$ travelled in time $t$ is given by $S = at^2 + bt + 6$. If the particle comes to rest after $4 \text{ s}$ at a distance of $16 \text{ m}$ from the starting point,then the acceleration of the particle is: